A Mean Field Based Methodology for Modeling Mobility in Ad Hoc Networks

Abstract:

In this paper we propose a methodology for the modeling and analysis of ad
hoc networks composed by a large number of nodes moving among geographical
regions. This methodology uses compositional construction of stochastic
Petri nets (SPN) for building the model which allows for specifying the
model and the required performance indices at a high level of abstraction.
As our aim is to consider real scenarios with several geographical regions
and non-trivial user behavior in each region, the size of the state space
of the model can easily grow too large to analyze with exact analytical
approaches or even with simulation. For this reason, we propose to carry
out the analysis by constructing the mean field approximation of the behavior
of the SPN. The approximation is provided by a set of ordinary
differential equations (ODE) that can be derived automatically from the SPN
and can be solved numerically with low computational effort even for large
models.

The methodology is illustrated on a case study, modeling application
spreading in a mobile environment. It will be shown that the approximate
results obtained by the mean field approach capture well the behavior of
the system.